A145849 - OEIS

%I #17 Dec 16 2018 06:40:45

%S 1,9,33,41,129,137,161,169,513,521,545,553,641,649,673,681,2049,2057,

%T 2081,2089,2177,2185,2209,2217,2561,2569,2593,2601,2689,2697,2721,

%U 2729,8193,8201,8225,8233,8321,8329,8353,8361,8705,8713,8737,8745,8833,8841,8865,8873,10241

%N a(n) = A145812(2n-1).

%C Every positive odd integer m==3 (mod 8) is a unique sum of the form a(s)+2a(t), while other odd integers are not expressible in this form.

%H Vincenzo Librandi, <a href="/A145849/b145849.txt">Table of n, a(n) for n = 1..5000</a>

%F If f(x) = Sum_{n>=1}x^a(n), abs(x) < 1, then f(x)*f(x^2) = x^3/(1 - x^8).

%t a[n_] := 2 * FromDigits[IntegerDigits[2*n-2, 2], 4] + 1; Array[a, 50] (* _Amiram Eldar_, Dec 16 2018 *)

%o (PARI) a145812(n) = 2*fromdigits(binary(n-1), 4) + 1;

%o a(n) = a145812(2*n-1); \\ _Michel Marcus_, Dec 13 2018

%Y Bisection of A145812.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Oct 21 2008

%E More terms from _Michel Marcus_, Dec 13 2018